# Willingness to accept

In economics, willingness to accept (WTA) is the minimum amount of money that а producer (a seller) is willing to accept to sell a good or service, or to put up with something negative, such as pollution. This is in contrast to willingness to pay (WTP), which is the maximum amount of money a consumer (a buyer) is willing to sacrifice to purchase a good/service or avoid something undesirable. The price of any transaction will thus be any point between a buyer's willingness to pay and a seller's willingness to accept, the net difference of which is known as economic surplus.

Several methods have been developed to measure consumer willingness to pay or accept payment. These methods can be differentiated by whether they measure consumers' hypothetical or actual willingness to pay/accept, and whether they measure consumer willingness to pay/accept directly or indirectly.

Choice modelling techniques may be used to estimate the value of the WTP or WTA through a choice experiment.

Unlike WTP, WTA is not constrained by an individual's wealth. For example, the willingness to pay to stop the ending of one's own life can only be as high as one's wealth, while the willingness to accept compensation to accept the loss of one's life would be an extremely high number (or maybe infinite, meaning that there would be no finite acceptable payment amount).

## Formal definition

Let u(w, x) be an individual's utility function, where w is the person's wealth and x is a dummy variable that takes the value 1 in the presence of an undesired feature and takes the value 0 in the absence of that feature. The utility function is assumed to be increasing in wealth and decreasing in x. Also, define w0 as the person's initial wealth. Then the willingness to accept is defined by

${\displaystyle u(w_{0}+WTA,1)=u(w_{0},0).}$ [1]

That is, the willingness to accept payment in order to put up with the adverse change equates the pre-change utility (on the right side) with the post-change utility, including compensation.

In contrast, the willingness to pay is defined by

${\displaystyle u(w_{0}-WTP,0)=u(w_{0},1).}$

That is, the willingness to pay to avoid the adverse change equates the post-change utility, diminished by the presence of the adverse change (on the right side), with utility without the adverse change but with payment having been made to avoid it.

The concept extends readily to a context of uncertain outcomes, in which case the utility function above is replaced by the expected value of a von Neumann-Morgenstern utility function (See expected utility hypothesis).

## Standard theory versus experimental results

The standard assumptions of economic theory imply that when income effects are small, the gap between WTP and WTA should be negligible. Thus indifference curves are drawn without reference to current endowments. This leads to the wide acceptance of the Coase theorem assertion that, subject to income effects, the allocation of resources will be independent of the assignment of property rights when costless trades are possible. This is to say, the allocation of property rights does not influence the way externalities are internalized by the market. However, many experiments, such as that by Daniel Kahneman, Jack L. Knetsch and Richard Thaler showed that measures of WTA greatly exceed measures of WTP.[2] Another well-known example was documented by Ziv Carmon and Dan Ariely, who found that willingness to accept for tickets to a major basketball game was more than 10 times larger than the willingness to pay.[3] One explanation is that the endowment effect makes people value a good or service more if they possess it.

The endowment effect theory's conclusions about the relationship between WTA-WTP has recently come under criticism.[4][5][6] Plott and Zeiler argued that "...observed gaps [between WTA and WTP] are symptomatic of subjects' misconceptions about the nature of the experimental task" and that "the differences reported in the literature reflect differences in experimental controls for misconceptions as opposed to differences in the nature of the commodity."[4] As a consequence of this work, alternative theories regarding the endowment effect and WTA-WTP correlations have become more widespread, as it may be possible that some economic scholarship about the WTA-WTP gaps are a result of experimental design issues.[4][7]

## Applications

WTP and WTA are important factors for public policy. Many economic decisions are based upon the implicit assignment of property rights. When looking at a lake which is being polluted by a nearby factory, the WTA and WTP for treatment of an effluent treatment plant may have different consequences based upon how property rights are politically assigned. If lakeside residents have no property right to an effluent-free lake, then their willingness to pay to treat the lake's water supply would be considered. Conversely, if the lakeside residents are found to have a property right to a clean lake, then their willingness to accept compensation for a polluted lake would be considered.